scholarly journals Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin-Mun Jeong ◽  
Seong Ho Cho
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Functional Differential Equations ◽  
Fractional Power ◽  
Regularity Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.

Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems

1991 ◽  
Vol 43 (5) ◽  
pp. 1098-1120 ◽  
Author(s):  
Jianhong Wu ◽  
H. I. Freedman
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Strong Monotonicity ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Monotone Dynamical Systems

AbstractThis paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Qi Li ◽  
Rui Wang ◽  
Fanwei Meng ◽  
Jianxin Han
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Third Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

The aim of this work is to discuss asymptotic properties of a class of third-order nonlinear neutral functional differential equations. The results obtained extend and improve some related known results. Two examples are given to illustrate the main results.

scholarly journals Oscillation theorems of solution of second-order neutral differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12771-12779
Author(s):  
Ali Muhib ◽  
◽  
Hammad Alotaibi ◽  
Omar Bazighifan ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Theoretical Support ◽  
Functional Differential ◽  
Oscillation Theorems ◽  
New Criteria ◽  
Oscillation Of Solutions

<abstract><p>In this paper, we aim to explore the oscillation of solutions for a class of second-order neutral functional differential equations. We propose new criteria to ensure that all obtained solutions are oscillatory. The obtained results can be used to develop and provide theoretical support for and further develop the oscillation study for a class of second-order neutral differential equations. Finally, an illustrated example is given to demonstrate the effectiveness of our new criteria.</p></abstract>

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

2012 ◽  
Vol 55 (4) ◽  
pp. 736-751 ◽  
Author(s):  
Eduardo Hernández ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Classical Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

AbstractIn this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

scholarly journals Oscillations of higher order neutral differential equations

1998 ◽  
Vol 64 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Neutral Functional Differential Equations ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Functional Differential ◽  
Image Position

AbstractSome new oscillation criteria for higher order neutral functional differential equations of the form n is even, are established.

scholarly journals EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

2008 ◽  
Vol 78 (3) ◽  
pp. 365-382 ◽  
Author(s):  
HERNÁN R. HENRÍQUEZ ◽  
MICHELLE PIERRI ◽  
PLÁCIDO TÁBOAS
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Qualitative Properties ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Bounded Continuous Function ◽  
Functional Differential

AbstractA bounded continuous function $u:[0,\infty )\to X$ is said to be S-asymptotically ω-periodic if $ \lim _{t\to \infty }[ u(t+\omega ) -u(t)]=0$. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.

scholarly journals Some neutral equations with a control parameter

1981 ◽  
Vol 23 (3) ◽  
pp. 383-394
Author(s):  
Vasil G. Angelov
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Continuous Dependence ◽  
Control Parameter ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Accretive Operators ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential

This paper presents sufficient conditions, involving accretive operators, for the existence, uniqueness and continuous dependence on a control parameter of the solutions of some initial and boundary value problems for neutral functional differential equations.

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